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Electronic transport properties of top-gated epitaxial-graphene nanoribbonfield-effect transistors on SiC wafers
Wan Sik Hwanga)
Department of Electrical Engineering, University of Notre Dame, Notre Dame, Indiana 46556and Department of Materials Engineering (MRI), Korea Aerospace University, Goyang 412791, Korea
Kristof Tahy and Pei ZhaoDepartment of Electrical Engineering, University of Notre Dame, Notre Dame, Indiana 46556
Luke O. NyakitiU.S. Naval Research Laboratory, Washington, DC, 20375, USA and Department of Marine Engineering,Texas A&M University, Galveston, Texas 77553
Virginia D. Wheeler, Rachael L. Myers-Ward, Charles R. Eddy, Jr, and D. Kurt GaskillU.S. Naval Research Laboratory, Washington, DC 20375
Huili (Grace) Xing, Alan Seabaugh, and Debdeep Jenab)
Department of Electrical Engineering, University of Notre Dame, Notre Dame, Indiana 46556
(Received 25 October 2013; accepted 23 December 2013; published 10 January 2014)
Top-gated epitaxial-graphene nanoribbon (GNR) field-effect transistors on SiC wafers were
fabricated and characterized at room temperature. The devices exhibited extremely high current
densities (�10 000 mA/mm) due to the combined advantages of the one-dimensionality of GNRs and
the SiC substrate. These advantages included good heat dissipation as well as the high optical phonon
energy of the GNRs and SiC substrate. An analytical model explains the measured family of ID–VDS
curves with a pronounced ‘kink’ at a high electric field. The effective carrier mobility as a function of
the channel length was extracted from both the ID–VDS modeling and the maximum transconductance
from the ID–VGS curve. The effective mobility decreased for small channel lengths (<1 lm),
exhibiting ballistic or quasiballistic transport properties. VC 2014 American Vacuum Society.
[http://dx.doi.org/10.1116/1.4861379]
I. INTRODUCTION
Graphene nanoribbons (GNRs) are being investigated as
a possible channel material for transistors as well as for
interconnects for future electron devices. This is because
graphene allows exceptional electrostatic control due to its
native two-dimensional (2D) confinement, and it also has a
high current carrying capacity with excellent thermal
conductivity.1–3 In many reports, graphene or GNRs sit on
SiO2 substrates, whose phonon energy (�57 meV)4 is signifi-
cantly below the longitudinal zone boundary phonon energy
(�160 meV) of intrinsic graphene.5 Therefore, the saturation
velocity of carriers in graphene field-effect transistors
(FETs) has been found to be limited by the remote phonon
scattering caused by the SiO2 substrate, and not by the intrin-
sic properties of graphene, indicating the importance of
substrate choice for graphene devices.6 In order to exploit
the inherent advantage of graphene, substrates with
higher phonon energies such as SiC (�100 meV)7 are attrac-
tive. In this paper, we report the measurement of very high
current densities (�10 mA/lm), differential conductance
(�1.3 mS/lm), and estimated transconductance (�1 mS/lm
@ VDS¼ 10 V) in epitaxial-graphene nanoribbon FETs
(EGNR-FETs) on SiC. Compared to GNRs on SiO2 sub-
strates (�2 mA/lm)8 and 2D graphene on SiC substrates
(�2 mA/lm),9 GNRs on SiC substrates show a far higher
current carrying capacity because the substrates show effi-
cient heat dissipation and higher optical phonon energy. The
combined effect of GNRs and the SiC substrate allows the
EGNR-FETs to achieve the highest current density measured
in any semiconductor structures to date, including 2D gra-
phene. We model the high-field device characteristics and
extract the carrier mobility in the GNRs as a function of the
channel length. The numbers indicate ballistic or quasiballis-
tic transport properties as the channel length of the device is
scaled down below 1lm.
II. EXPERIMENTAL PROCEDURES
Epitaxial graphene (EG) was formed by thermal decom-
position of semi-insulating, nominally on-axis Si-face 6H-
SiC substrate coupons with square side lengths of 10 mm
using a commercial Aixtron VP508 SiC growth reactor at
1620 �C for a duration of 120 min in an Ar ambient at a con-
stant pressure of 100 mbar. Using a continuous process, sam-
ples were etched in hydrogen at temperatures 1520 �C for
50 min to attain a scratch-free SiC surface with uniform steps
and terraces before graphene synthesis.10 Pressure and tem-
perature stabilization when transitioning from hydrogen
etching to graphene synthesis in an Ar ambient took between
3 and 5 min. After growth, the samples were cooled in Ar to
800 �C in order to suppress unwanted Si sublimation and
limit contaminates that may adhere to the surface. This rec-
ipe yields a uniform epitaxial graphene layer that is repro-
ducible from run-to-run.10
a)Electronic mail: [email protected])Electronic mail: [email protected]
012202-1 J. Vac. Sci. Technol. B 32(1), Jan/Feb 2014 2166-2746/2014/32(1)/012202/5/$30.00 VC 2014 American Vacuum Society 012202-1
The EG was then patterned into 20 nm-wide nanoribbons
using electron-beam lithography (EBL). Finally, EGNR-
FETs with a 70 meV energy gap were fabricated.11 Figure
1(a) shows the schematic top and cross-sectional views of
the device structure. Source/drain electrodes were defined
using EBL. The Cr/Au (5/100 nm) was then deposited using
an electron-beam evaporation, and a lift-off process was car-
ried out. Atomic layer deposition Al2O3 of 20 nm was depos-
ited on the EGNRs using a 0.5 nm-thick oxidized evaporated
Al nucleation layer. A scanning electron microscope (SEM)
image of an EGNR in the channel is shown in Fig. 1(b) with
an inset depicting the Raman map of the graphene on the
SiC. The measured capacitance of the gate stack was
�0.3 lF�cm�2 with a 100 x 100 lm2 area.
III. RESULTS AND DISCUSSION
Figure 2(a) shows the measured ID versus VGS of the
20 nm-wide EGNR-FETs. The results indicate that the
EGNR-FETs shown-type behavior. A family of ID–VDS
curves at various VGS was correlated with the modeling (dis-
cussed below) in Fig. 2(b). The observed maximum current
density (�10 000 mA/mm) of the EGNR-FETs, as shown in
Fig. 2(b), is the highest current density ever reported from ei-
ther graphene-based FETs (Refs. 1, 12, and 13) or III-nitride
high-electron mobility transistors (HEMTs).14 The current
density was defined as current per unit GNR width (ID/W).
The current-carrying capacity of 2D graphene FETs has
been reported to be higher than traditional FETs and compa-
rable to III-Nitride HEMTs.13 The 1D transport of GNRs
enables EGNR-FETs to show the highest current density by
preventing lateral momentum in the graphene and enabling
the materials to benefit from the spreading of the 3D
heat.1 The efficient heat dissipation of the EGNR and SiC
substrate also contribute to the enhanced current density.
SiC has a very high thermal conductivity compared to SiO2
[SiC� 350 Wm�1K�1,15 SiO2� 1.3 Wm�1K�1,16 and sus-
pended graphene >4000 Wm�1K�1 (Ref. 17)] and this
reduces localized heating, which can generate resistive
defects.
The measured ID–VDS curves were compared with a
traditional long channel transistor model,18 where
COX¼ 0.29 lFcm�2, l¼ 950 cm2.V�1.s�2, and VT¼�12 V.
The COX, l, and VT are best fits, and those values are compa-
rable to the measured one. The measured ID only matched
well with the model in the linear region. However, the pro-
nounced “kink” at the large negative gate bias VGS¼�4 V
with the higher VDS was not captured. This revealed that the
behavior of the EGNR-FETs was predictable using the long
channel model in the linear region, but due to the narrow
band gap of the GNR, the saturation region equation was not
valid.
In order to model the pronounced “kink” accurately, the
analytical expression shown in Eq. (1)19 was used, where
n0¼ 9�1012 cm�2, l¼ 950 cm2�V�1�s�2, �SAT¼ 108 cm�s�1,
COX¼ 0.3 lF�cm�2, VDP¼�8.5 V, and RS¼ 1000 X
ID ¼el W=Lð Þ
ðVDS�IDRS
IDRS
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffin2
O þ COX VGS � VDP � VðxÞð Þ=e½ �2q
dVðxÞ
1þ l VDS � 2IDRSð Þ=LvSAT: (1)
The analytical model captures the measured ID in all VDS
regions, as shown in Fig. 2(b). Figure 2(c) shows the differ-
ential conductance as a function of VDS at two different VGS
values: VGS¼ 6 V and VGS¼�4 V. On the one hand, at
VGS¼ 6 V (region I), the Fermi level is far above the charge
neutrality point so that the Fermi level in the channel
remains above the neutral point for the drain voltages used,
and thus, electrons are the major carrier over the entire VDS
region. The decrease in the differential conductance is due to
scattering as the electric field increases. On the other hand,
FIG. 1. (Color online) (a) Schematic device structure of the top-gated
EGNR-FETs with parasitic resistances (RS¼RAþRC) aside from the intrin-
sic resistance of GNR (RCH). (b) SEM image of a 20 nm-wide GNR covered
by an HSQ mask with the top right insert showing a bird’s eye view of the
representative device structure before deposition of the gate dielectric and
gate metal. The bottom insert shows a Raman map of I2D/IG image indicat-
ing the uniformity of the epigraphene on the SiC.
012202-2 Hwang et al.: Electronic transport properties of top-gated epitaxial-graphene 012202-2
J. Vac. Sci. Technol. B, Vol. 32, No. 1, Jan/Feb 2014
at VGS¼�4 V, the Fermi level is just above the charge neu-
trality point, and the differential conductance shows three
distinct behavior regimes (II, III, and IV) as illustrated in
Fig. 2(d). At a low electric field (VDS� 4 V, region II), the
channel near the drain is influenced to a lesser degree by the
drain voltage, and the electrons are still the major carriers.
However, at a high electric field (VDS 7 V, region IV), the
channel near the drain is significantly influenced by the drain
voltage, and holes become the major carrier type in the chan-
nel near the drain since the Fermi level moves below the
charge neutrality point. The differential conductance then
increases as the electric field increases due to the increase in
the number of hole carrier density. Region III is thus the
transition region.
Using the analytical modeling applied in Fig. 2(b), the
channel length dependence of mobility was then explored.
Figure 3(a) shows a comparison of the modeled ID with
constant mobility and the measured ID as a function of the
channel length. In the case of long channel devices
(L¼ 3 lm and 5 lm), the model matches well with the ex-
perimental results. However, the discrepancy between the
model and experiment increases as the channel length
decreases. This indicates that the effective mobility param-
eter of a short channel model should be smaller than that of
a long channel model in order to match the modeling with
experimental results (L< 1 lm). Figure 3(b) shows the
ID–VDS plot at VGS¼ 0 V at various channel lengths. In
order to match the measured ID with the modeled ID, the
effective mobility is varied as a single fitting parameter
while other parameters are fixed to be the same as the val-
ues used in Fig. 2(b).
The effective low-field mobility was also extracted
from the maximum transconductance (gm) of the ID–VGS
curve (not shown) as a function of the channel length, as
shown in Fig. 3(c). Figure 3(d) shows the effective mobil-
ity as a function of channel length, where the effective mo-
bility were extracted both from the ID–VDS fitting, as
shown in Fig. 3(b), and the maximum gm of the ID–VGS, as
shown in Fig. 3(c). The effective mobility trend from these
different methods clearly shows that mobility degrades sig-
nificantly as the channel length is scaled down below 1 lm.
This indicates that the channel length becomes comparable
to the mean free path and an onset of quasiballistic trans-
port properties, where the mobility is expected to be
degraded. A ballistic mean free path can be extracted
from20
lEffective ¼ l0 � L=ðkþ LÞ; (2)
where l0¼ the mobility of a long channel device
(700 cm2�V�1�s�2) from Fig. 3(d), k¼mean free path, and
L¼ channel length. From this relation, the extracted mean
free path (k) is between 100 and 800 nm for EGNR-FETs,
comparable to 300 6 100 nm for 2D graphene FETs.20 It
should be noted that parasitic capacitance, scattering, and
the internal junction of the metal/graphene with a scaling
FIG. 2. (Color online) Transport properties of top-gated 20 nm-wide EGNR-FET. (a) ID–VGS characteristics at VDS¼ 0.02 V. (b) Analytical model (line,
discussed in text), long channel mode (dashed line), and measured ID–VDS characteristics (dotted line) with VGS varied from 6 V to �4 V. (c) Differential con-
ductance as a function of drain-to-source voltage (VDS) at VGS¼ 6 V and �4 V. (d) Schematic drawing of the carrier concentration in the channel regions at
VGS¼ 6 V (I) and �4 V (II, III, and IV), respectively.
012202-3 Hwang et al.: Electronic transport properties of top-gated epitaxial-graphene 012202-3
JVST B - Microelectronics and Nanometer Structures
down of the GNR channel length were neither discussed nor
considered in the modeling. These factors lead to some
uncertainty to the mean free path in the GNRs.
IV. CONCLUSIONS
Top-gated EGNR-FETs were fabricated and character-
ized at room temperature. These devices exhibited very
high current densities (�10 mA/lm) and conductance
(�1.3 mS/lm) due to the combined advantages of the
GNRs and SiC substrate—namely, the excellent heat dissi-
pation and high optical phonon energies. The transistor
characteristics were explained using an analytical model,
and the extracted effective mobility showed comparable
behavior to 2D graphene. The effective mobility degraded
as the channel length decreased below 1lm, where the qua-
siballistic transport begins to contribute.
ACKNOWLEDGMENTS
This work was supported by the Semiconductor Research
Corporation (SRC), Nanoelectronics Research Initiative
(NRI), and the National Institute of Standards and
Technology (NIST) through the Midwest Institute for
Nanoelectronics Discovery (MIND), STARnet, an SRC pro-
gram sponsored by MARCO and DARPA, and by the Office
of Naval Research (ONR) and the National Science
Foundation (NSF). L. O. Nyakiti acknowledges the support
of the American Society for Engineering Education/Naval
Research Laboratory Postdoctoral Program. Work at the US
Naval Research Laboratory was supported by ONR.
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